Base area and volume of solid right circular cylinder are 13.86 sq. cm and 69.3 cu. cm respectively. Find the height and curved surface area of the cylinder. (Take π = 22/7)

Let's denote the height of the cylinder as 'h', the radius as 'r', the base area as 'A', and the volume as 'V'.

We are given:
Base area (A) = 13.86 sq. cm
Volume (V) = 69.3 cu. cm
Value of pi (π) = 22/7

We know the formula for the base area and volume of a right circular cylinder:

Base area (A) = π * r^2
Volume (V) = π * r^2 * h

Let's start by finding the radius (r) of the cylinder:

13.86 sq. cm = π * r^2

Now, let's calculate the radius (r):

r^2 = 13.86 / π
r^2 = 13.86 / (22/7)
r^2 = 13.86 * (7/22)
r^2 = 4.41
r = √4.41
r ≈ 2.1 cm (rounded to one decimal place)

Next, we'll find the height (h) using the volume formula:

69.3 cu. cm = π * (2.1 cm)^2 * h

Now, let's calculate the height (h):

h = 69.3 / (π * 2.1^2)
h = 69.3 / (22/7 * 2.1^2)
h = 69.3 / (22/7 * 4.41)
h = 69.3 / 12.54
h ≈ 5.53 cm (rounded to two decimal places)

So, the height of the cylinder is approximately 5.53 cm.

Now, let's find the curved surface area (CSA) of the cylinder. The formula for the curved surface area of a right circular cylinder is:

Curved Surface Area (CSA) = 2 * π * r * h

Let's calculate the curved surface area (CSA):

CSA = 2 * π * 2.1 cm * 5.53 cm
CSA = 2 * (22/7) * 2.1 cm * 5.53 cm
CSA = 2 * (22/7) * 11.613 cm^2
CSA ≈ 145.94 sq. cm (rounded to two decimal places)

So, the curved surface area of the cylinder is approximately 145.94 sq. cm.